Abstract:
A well-known analogy of the flow of viscous incompressible fluid and incompressible elastic medium. According to this analogy, the solution of the equations of the elasticity theory with the Poisson's ratio nu = 0; 5 and for any fixed shear modulus mu can be interpreted as a motion of a viscous incompressible fluid with viscosity mu. Thus, we can consider the usual static linear elasticity task with Hooke's law at lambda -> infinity, as a mathematical model of approaching to incompressible medium. In this paper, we obtained the asymptotic lambda -> infinity. Estimation of the proximity of the solution of an elastic static problem with Hooke's law to the solution of incompressible medium (Stokes problem). The final estimate allows to use well-known difference schemes and algorithms for an elastic compressible medium to solve incompressible medium. In this paper, an estimate of the proximity of the solutions of these problems is proved at lambda -> infinity, i.e. (u ->(u) over barH)(lambda ->infinity) (lambda div (u) over bar ->-p)(lambda ->infinity) (sigma ->sigma H)(lambda ->infinity). To substantiate this fact in [1-3], various methods for the first boundary value problem were investigated. For the static problem of the theory of elasticity, there is currently a whole series of papers devoted to numerical implementation using difference schemes. In paper [4], the estimate O(lambda(-alpha)) where k = 1/2 was obtained, in the proposed paper the estimate O(lambda(-1)), and in further work we will show that this estimate is best possible in order
